SOLUTION: A farmer has 40 metres of fencing with which he intends to make a rectangular enclosure for a few sheep and their lambs. The farmer calculates that he requires 96m²of grass in the

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Question 648113: A farmer has 40 metres of fencing with which he intends to make a rectangular enclosure for a few sheep and their lambs. The farmer calculates that he requires 96m²of grass in the sheep pen. By forming a quadratic equation find the dimensions of the pen
Answer by stanbon(75887) About Me  (Show Source):
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A farmer has 40 metres of fencing with which he intends to make a rectangular enclosure for a few sheep and their lambs. The farmer calculates that he requires 96m²of grass in the sheep pen. By forming a quadratic equation find the dimensions of the pen
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Perimeter = 2(L + W) = 40 metres
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Area = L*W = 96 m^2
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Solve the 1st equation for "L":
L + W = 20
L = 20-W
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Sustitute into the 2nd equation and solve for "W":
(20-W)W = 96
20W-W^2 = 96
W^2 - 20W + 96 = 0
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(W -16)(W-4) = 0
Width = 16 m or Width = 4 m
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If W = 16, then L = 4
If W = 4, then L = 16
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Cheers,
Stan H.
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